Exact solutions for internuclear vectors and backbone dihedral angles from NH residual dipolar couplings in two media, and their application in a systematic search algorithm for determining protein backbone structure.

Lincong Wang and Bruce R. Donald

Journal of Biomolecular NMR, 2004; 29: 223-242.

A flow chart illustrating the algorithm. A chart illustrating the three major stages (delimited by two dashed lines) of the algorithm beginning with the input RDC data and ideal helix and strand models to a final three dimensional backbone structure. RDCs refer to NH RDCs measured in two media. As stated in the main text, to improve accuracy, alignment tensors are computed twice in Stage I. DFS refers to depth-first search and SVD refers to singular value decomposition.

A flow chart of a single step of the DFS-based refinement stage. The three major phases are delimited by two dashed lines. The six angles are defined in the main text. The quartic and trigonometric equations refer, respectively, to Equations 4, 5. The Ramachandran filter represents filtering through the favorable Ramachandran regions and the Gaussian convolution corresponds to the simulation of the experimental error by a Gaussian distribution with the experimental value (DNH,i or DNH,i) as its mean and the error as its variance. Many such steps are required for refining a secondary structure element as shown by a dashed arrow.